Data Envelopment Analysis

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Data Envelopment Analysis (DEA). A nonparametric method in operations research and econometrics for multivariate frontier estimation and ranking.

With the intention of being consistent with microeconomic production theory and when being conscious of the existence of inefficiencies in the production processes, frontier techniques have been developed during the last 30 years.

Among the different solutions, we can find a nonparametric method called Data Envelopment Analysis (DEA), which is a linear programming methodology to measure the efficiency of multiple Decision Maker Units (DMUs) when the production process presents a structure of multiple inputs and outputs.

Then, some of the benefits of it are: (1) there is no need to explicitly specify a mathematical form for the production function, (2) it has proven to be useful in uncovering relationships that remain hidden for other methodologies, (3) is capable of handling multiple inputs and outputs, (4) it can be used with any input-output measurement, (5) the sources of inefficiency can be analysed and quantified for every evaluated unit.

In the DEA methodology, formerly developed by Charnes, Cooper and Rhodes (1978), efficiency is defined as a weighted sum of outputs to a weighted sum of inputs, where the weights structure is calculated by means of mathematical programming and constant returns to scale are assumed. In 1984, Banker, Charnes and Cooper developed a model with variable returns to scale.

[edit] Inefficiency measuring with DEA

Data Envelopment Analysis (DEA) has been recognized as a valuable analytical research instrument and a practical decision support tool. DEA has been credited for not requiring a complete specification for the functional form of the production frontier nor the distribution of inefficient deviations from the frontier. Rather, DEA requires general production and distribution assumptions only. However, if those assumptions are too weak, inefficiency levels may be systematically underestimated in small samples. In addition, erroneous assumptions may cause inconsistency with a bias over the frontier. Therefore, the ability to alter, test and select production assumptions is essential in conducting DEA-based research. However, the DEA models currently available offer a limited variety of alternative production assumptions only.

[edit] The traditional DEA framework

In DEA, the performance of decision making units (henceforth DMUs) is evaluated against an empirical approximation for the production possibility set (henceforth PPS). The PPS is defined as the set of all combinations of inputs and outputs that are attainable given the current production technology. P= {(y, x): y can be produced from x} That set is approximated using a set of observations on inputs and outputs for n DMUs (j=1,…,n). The standard Charnes, Cooper and Rhodes (1978) model is based on the assumption that the true production technology is characterized by constant returns-to-scale (henceforth CRS). For each evaluated DMU, a reference unit is selected from the approximating set. These reference units can be used for efficiency estimation and performance benchmarking purposes. The input-output combination of the evaluated unit relative to that of the reference unit can be used for evaluating the efficiency of past operations and for assessing potential improvements for future operations. The units that constitute the reference unit are potential benchmark partners. In addition, comparing the production process of the evaluated unit with that of the benchmark partners can reveal causes for past inefficiencies and remedies for future improvements. Whereas the structure of the approximating set depends on the assumptions imposed on the production technology and the distribution of observations, the selection of a particular reference unit from that set depends on the preferences of the evaluating manager. It is generally difficult to reliably elicit managerial preferences, and moreover properly incorporate preferences in an optimization problem. However, using certain assumptions about the general characteristics of the preference structure, the decision problem can be simplified. An assumption that is implicit in most DEA models is that the evaluator prefers more over less for the referencing outputs and less over more for the inputs. In our opinion, that is a valid assumption, because the purpose of the reference units is to assess inefficiency and potential performance improvements relative to the production possibilities, and moreover a unit gives a better representation of those possibilities if its outputs are higher and its inputs are lower. If the above assumption holds, all composite units that are dominated by other units, i.e. units that produce more output with the or less input or alternatively consume less input for equal or more output, can be discarded as decision alternatives. Only non-dominated units have to be considered as potential reference units. We will refer to those units as the CCR admissible set.